We define a one parameter family of quasi-local mass functionals mc (Σ), 0 ≤ c ≤ ∞, which are nondecreasing on surfaces in 3-manifolds with nonnegative scalar curvature with respect to a one parameter family of flows. In the case that c = 0, m0(Σ) equals the Hawking mass of Σ2 and the corresponding flow is inverse mean curvature flow. Then, following the arguments of Geroch [8], Jang and Wald [12], and Huisken and Ilmanen [9], we note that the generalization of their results for inverse mean curvature flow would imply that if mADM is the total mass of the complete, asymptotically flat 3-manifold with nonnegative scalar curvature, then mADM ≥ mc(Σ) for all nonnegative c and all connected surfaces Σ which are not enclosed by surfaces with less area.